Fang-Rong Hsu

An optimal algorithm for finding the minimum cardinality dominating set on permutation graphs

A dominating set D of an undirected graph G is a set of vertices such that every vertex not in D is adjacent to at least one vertex in D. Given a undirected graph G, the minimal cardinality dominating set problem is to find a dominating set of G with minimum number of vertices. The minimal cardinality dominating set problem is NP-hard for general graphs. For permutation graphs, the best-known algorithm ran in O(n log log n) time, where n is the number of vertices. In this paper, we present an optimal O(n) algorithm.

Efficient algorithms for the minimum connected domination on trapezoid graphs

Given the trapezoid diagram, the problem of finding the minimum cardinality connected dominating set in trapezoid graphs was solved in O(m+n) time [Y.D. Liang, Steiner set and connected domination in trapezoid graphs, Inform. Process. Lett. 56 (2) (1995) 101-108]. Kohler [E. Kohler, Connected domination and dominating clique in trapezoid graphs, Discr. Appl. Math. 99 (2000) 91-110] recently improved this result to O(n) time. For the (vertex) weighted case, the problem of finding the minimum weighted connected dominating set in trapezoid graphs can be solved in O(m+nlogn) time [Anand Srinivasan, M.S. Chang, K. Madhukar, C. Pandu Rangan, Efficient algorithms for the weighted domination problems on trapezoid graphs, Manuscript, 1996]. Herein n (m) denotes the number of vertices (edges) of the trapezoid graph. In this paper, we show a different approach for the problem of finding the minimum cardinality connected dominating set in trapezoid graphs using O(n) time. For finding the minimum weighted connected dominating set, we show the problem can be solved in O(nloglogn) time.

The on-line first-fit algorithm for radio frequency assignment problems

The radio frequency assignment problem is to minimize the number of frequencies used by transmitters with no interference in radio communication networks; it can be modeled as the minimum vertex coloring problem on unit disk graphs. In this paper, we consider the on-line first-fit algorithm for the problem and show that the competitive ratio of the algorithm for the unit disk graph G with χ(G) = 2 is 3, where χ(G) is the chromatic number of G. Moreover, the competitive ratio of the algorithm for the unit disk graph G with χ(G) < 2 is at least 4 - 3/χ(G). The average performance for the algorithm is also discussed in this paper.

The application of alternative splicing graphs in quantitative analysis of alternative splicing form from EST database

Alternative splicing of a single pre-mRNA can give rise to different mRNA transcripts. Alternative splicing of pre-messenger RNA is an important layer of gene expression regulation in eukaryotic cell. Consequently, alternative splicing is an important mechanism for generating protein diversity from a single gene. Although alternative splicing is an important biological process, standard molecular biology techniques have only identified several hundred alternative splicing variants and create a bottleneck in terms of experimental validation. In this paper, we propose methods of obtaining models of weighted alternative splicing graphs and ways of generating all alternative splicing forms from a weighted alternative splicing graph and formulate linear programming models and use the popular linear programming solver to obtain the quantitative distributions of various alternative splicing forms. Basically, the method uses the UniGene clusters of human expressed sequence tags (ESTs) to identify alternative splicing sites. Furthermore, we propose linear time algorithms that correctly produce all possible alternative splicing variants with their corresponding probabilities. Using these methods, we infer several sets of putative alternative splicing forms; these results are then compared with methods proposed by others. Then by aligning sequences of EST database to the genomic data, we identify locations of exons as well as the alternative splicing sites. To quantify these putative alternative splicing forms, we choose segments in genome to count the EST number, and combine the information of EST and alternative splicing form by constructing the suitable linear programming model.

Genome-wide alternative splicing events detection through analysis of large scale ESTs

In the past several years, the analysis of alternative splicing and its application to identify the origins of disease has been gaining momentum. Therefore, we developed a value added transcriptome database (Avatar). We mapped EST (expressed sequence tag) and mRNA sequences onto whole human genomic sequence. We identified 9,937 alternative splicing relationships genes through an analysis of large-scale ESTs. Besides, we provided alternative splicing information for six organisms: Homo sapiens, Mus musculus, Rattus norvegiens, Caenorhabditis elegans, Drosophila melanogaster and Arabidopsis thaliana.

Extracting Alternative Splicing Information from Captions and Abstracts Using Natural Language Processing

Alternative splicing mechanisms provide protein diversity for cellular growth and development. In this research, we generate a database to descript alternative splicing in different circumstance from captions and abstracts in open access journals by using natural language processing techniques. We use medical subject headings(MeSH) to tag words, and extract the AS mechanism information by UMLS semantic network. In this database, AS information in genes on tissue-specificity, disease-related, developmental stage, functional implications, splicing type and species are contained.

Parallel Algorithms for Shortest Paths and Related Problems on Trapezoid Graphs

In this paper, we consider parallel algorithms for shortest paths and related problems on trapezoid graphs under the CREW PRAM model. Given a trapezoid graph with its corresponding trapezoid diagram, we present parallel algorithms solving the following problems: For the single-source shortest path problem, the algorithm runs in O(log n) time using O(n) processors and space. For the all-pair shortest path query problem, after spending O(log n) preprocessing time using O(n log n) space and O(n) processors, the algorithm can answer the query in O(log δ) time using one processor. Here δ denotes the distance between two queried vertices. For the minimum cardinality Steiner set problem, the algorithm runs in O(log n) time using O(n) processors and space. We also extend our results to the generalized trapezoid graphs. The single-source shortest path problem and the minimum cardinality Steiner set problem on d-trapezoid graphs and circular d-trapezoid graphs can both be solved in O(log n log d) time using O(nd) space and O(d2n= log d) processors. The all-pair shortest path query problem on d-trapezoid graphs and circular d-trapezoid graphs can be answered in O(d log δ) time using one processor after spending O(log n log d) preprocessing time using O(nd log n) space and O(d2n= log d) processors.

An Optimal Algorithm for Finding the Minimum Cardinality Dominating Set on Permutation Graphs

A dominating set D of an undirected graph G is a set of vertices such that every vertex not in D is adjacent to at least one vertex in D. Given a undirected graph G, the minimal cardinality dominating set problem is to find a dominating set of G with minimum number of vertices. The minimal cardinality dominating set problem is NP-hard for general graphs. For permutation graphs, the best-known algorithm ran in O(n log log n) time, where n is the number of vertices. In this paper, we present an optimal O(n) algorithm.

An optimal EREW parallel algorithm for computing breadth-first search trees on permutation graphs

Given a undirected graph G, the breadth-first search tree is constructed by a breadth-first search on G. In this paper, an optimal parallel algorithm is presented for constructing the breadth-first search tree for permutation graphs in O(log n) time by using O(n/log n) processors under the EREW PRAM model, where n is the number of nodes of the graph.

PARALLEL ALGORITHMS FOR COMPUTING THE CLOSEST VISIBLE VERTEX PAIR BETWEEN TWO POLYGONS

In this paper, we are concerned with the closest visible vertex pair problem, which is defined as follows: we are given two simple non-intersecting polygons P and Q with m and n vertices respectively, we are asked to find a closest visible pair of vertices between P and Q. We shall show that we can solve this problem in O(log(m+n)) time with O(m+n) processors in the CREW PRAM model.